This makes sense and you can get the same result if you change the resistors to be 100. Now the obvious curiosity is what range should you prefer to use; a higher ohm resistor or lower? 10k or 100? The choice seems important when determining what type of resistor you want to use , i.e. 1/8w, 1/4w, 1/2w etc...

Another example:Let's say we use the 100 ohm resistor from above hooked up to that 10v input. So first we need the current I. Using Ohm's Law I = V / R, so I = 10 / 100 making I = 0.1.

To get the watt rating (power) we again use Ohm's but this time it's P = I * V, so P = 0.1 * 10 making P = 1 watt.

Two resistors would therefore need to support 0.5 watts between the both of them to work properly. So when making a voltage divider with such low resistor values you'll actually want to use larger resistors that support a higher power rating, otherwise it will not dissipate enough heat and will likely fail (i.e. catch fire).

Now, if we had used 10kOhm resistors the math would work out to:I = 10 / 10000I = 0.001 amp

P = 0.001 * 10P = 0.01 watt

This voltage divider could use resistors rated for 1/8 watt 10kOhm.

Am I making valid assumptions? Am I missing anything or does this all add up?

The practical consideration in all this is when buying resistors in bulk it might be fine to just buy the cheaper 1/4 watt resistors at a higher ohm rating than wasting money on the higher watt resistors (which cost quite a bit more).

You're correct, in general a voltage divider should use large resistors to minimize wasted current in the resistors themselves, and minimize power dissipation. Of course, it also matters where the voltage divider is going...if there is non-trivial current being sourced then lower-value resistors will maintain a voltage closer to what you expect.

The absolute value of the resistors determines the output impedance of the voltage you generate with the potential divider. As a rough rule of thumb you should aim for ten times more current down the resistor chain as you aim to take out of it. Even then the actual voltage will change if you take a varying amount of current from it. This is why it is no good for powering devices.

The effective output impedance is the result of the two resistors in the chain connected in parallel.